Current and future constraints on the expansion history of the GREA model

In this work, we investigate the General Relativistic Entropic Acceleration (GREA) framework, in which late-time acceleration emerges from entropy production associated with the cosmological horizon, and compare its performance with the standard \(\Lambda\)CDM description of the Universe. We first confront GREA with current background observations, including baryon acoustic oscillations, type Ia supernovae, compressed CMB information, and cosmic chronometers, with particular emphasis on the geometric horizon parameter \(\sqrt{-k}\eta_0\). We then introduce a phenomenological extension of the theory by allowing for an additional dark energy component, \(\Omega_{de}\), enabling the recovery of a \(\Lambda\)CDM-like expansion history as a limiting case. We perform a Bayesian parameter inference and model comparison analysis using both current data and mock datasets representative of future surveys, including SKAO, LSST, and ET. While current data statistically prefer \(\Lambda\)CDM when compressed CMB information is included, GREA remains competitive for low-redshift combinations. Forecasts indicate that gravitational wave standard sirens are expected to enhance the ability to discriminate between entropic-driven and dark-energy-driven expansion scenarios, and to identify the underlying cosmological model favored by the data.